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On the number of integer points in translated and expanded polyhedra (1805.03685v2)
Published 9 May 2018 in math.CO and cs.CC
Abstract: We prove that the problem of minimizing the number of integer points inparallel translations of a rational convex polytope in $\mathbb{R}6$ is NP-hard. We apply this result to show that given a rational convex polytope $P \subset \mathbb{R}6$, finding the largest integer $t$ s.t. the expansion $tP$ contains fewer than $k$ integer points is also NP-hard. We conclude that the Ehrhart quasi-polynomials of rational polytopes can have arbitrary fluctuations.